Theorem pm4.71d

Description: Deduction converting an implication to a biconditional with conjunction. Deduction from Theorem *4.71 of WhiteheadRussell p. 120. (Contributed by Mario Carneiro, 25-Dec-2016)

	Ref	Expression
Hypothesis	pm4.71rd.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
Assertion	pm4.71d	$$⊢\phi \to \left(\psi \leftrightarrow \left(\psi \wedge \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		pm4.71rd.1	$$⊢\phi \to \left(\psi \to \chi \right)$$
2		pm4.71	$$⊢\left(\psi \to \chi \right)\leftrightarrow \left(\psi \leftrightarrow \left(\psi \wedge \chi \right)\right)$$
3	1 2	sylib	$$⊢\phi \to \left(\psi \leftrightarrow \left(\psi \wedge \chi \right)\right)$$